The allowance, which is almost double the previous £4,800-a-year limit for unreceipted claims, is paid on top of expenses for mortgage interest, rent, council tax and utility bills.

It has been approved without any public announcement or debate in Parliament as MPs leave for their summer holidays. Instead it has been agreed by a small committee of MPs chaired by John Bercow, the new Speaker, and including Harriet Harman, the Labour Leader of the House and Alan Duncan, the Tory frontbencher.

In the wake of the expenses scandal, Gordon Brown and David Cameron both pledged to clean up the system of parliamentary expenses. Mr Bercow had campaigned to replace Michael Martin by promising reform and Miss Harman and Mr Duncan had both said that expense claims which were not backed up by receipts would be unacceptable.

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However, the new rules state that “no receipts are necessary” for the subsistence payments and that it is “for members to decide” how the money is spent.

MPs will simply have to state how many nights they have spent away from their main home “on parliamentary business” to receive the flat-rate sum. There is no way for the information to be independently verified.

The Daily Telegraph has highlighted cases of MPs who spend almost no time at their designated main home and who would therefore be eligible to claim thousands of pounds a year. Previously, MPs could claim up to £400 a month without receipts for “food” when away from their main home.

Under the new system they could theoretically claim £775 if they said that they had stayed away from their main home for an entire month.

An MP who stayed away from their designated main home for an entire year — as Ann and Alan Keen, the married Labour MPs did — could claim £9,125 a year on top of mortgage interest payments under the new system.

The subsistence payments are disclosed in the new parliamentary Green Book – which sets out expense rules – issued to MPs on July 13.

The Green Book is usually revised only every few years, although a special edition has been produced following the expenses scandal. However, no announcement was made that a new Green Book was being produced.

At the height of the expenses scandal, high-profile announcements were made by Parliament on the scrapping of expense claims for furnishings and renovations, along with a cap on the amount of mortgage interest that could be claimed. But the subsistence payments were not publicly discussed. Instead they are included in the new Green Book, a copy of which was discreetly placed on the parliamentary website as MPs left for their 82-day summer break.

The fact that such a substantial amount has been agreed by MPs without public debate is certain to anger voters further.

The introduction of the new Green Book is one of Mr Bercow’s first acts as Speaker, and may undermine his claims to be reforming Parliament.

Changes to the House of Commons regulations are decided upon by a small committee of six MPs including Miss Harman and Mr Duncan. Both MPs have publicly stated that it is unacceptable for expense claims to be paid without receipts. Miss Harman said in the spring: “There would need to be receipts for all claims. I really do think that that is something sensible which we could decide for ourselves now.”

Mr Duncan previously said: “The second home allowance was often just paid once a month without receipts, which is an unacceptable system in the modern age.”

The subsistence payments are likely to raise concerns that MPs are seeking to limit public exposure of how they spend their allowances.

Under Freedom of Information laws, MPs have to publish receipts accompanying expense claims. These receipts — exposed by The Daily Telegraph in recent months — disclosed that MPs were claiming for everything from moat clearance and duck houses to dog food and chocolates.

However under the new system, how they spend the money will not be subject to public scrutiny. The new rules, sent to MPs, state: “Members... may claim a flat-rate sum of £25 for subsistence. No receipts are necessary for this claim to be made. How members spend the subsistence allowance is for them to decide.”

The maximum that MPs can claim for second home costs this year is £24,222, compared to £24,006 they were able to claim under the second homes allowance last year.